A local continuum model of cell-cell adhesion

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Nonlinear higher-order PDEs (35G20) Developmental biology, pattern formation (92C15) Cell biology (92C37) Pattern formations in context of PDEs (35B36)

Cites Work

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Stationary states of quadratic diffusion equations with long-range attraction
The importance of volume exclusion in modelling cellular migration
Nonlinear degenerate cross-diffusion systems with nonlocal interaction
Large systems of interacting particles and the porous medium equation
Volume effects in the Keller--Segel model: energy estimates preventing blow-up
A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion
Linear stability of selfsimilar solutions of unstable thin-film equations
On the diffusion of biological populations
Linear stability of steady states for thin film and Cahn-Hilliard type equations
Energy levels of steady states for thin-film-type equations
Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles
Topological graph description of multicellular dynamics based on vertex model
Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
Modeling stripe formation on growing zebrafish tailfins
A continuum approach to modelling cell-cell adhesion
Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation
Continuous models for cell-cell adhesion
On fully practical finite element approximations of degenerate Cahn-Hilliard systems
Biological Aggregation Driven by Social and Environmental Factors: A Nonlocal Model and Its Degenerate Cahn--Hilliard Approximation
Measure solutions for non-local interaction PDEs with two species
Convergence of a fully discrete and energy-dissipating finite-volume scheme for aggregation-diffusion equations
A Family of Nonlinear Fourth Order Equations of Gradient Flow Type
Long-wave instabilities and saturation in thin film equations
Thin Films with High Surface Tension
Convergence of a One-Dimensional Cahn--Hilliard Equation with Degenerate Mobility
Zoology of a Nonlocal Cross-Diffusion Model for Two Species
Properties of steady states for thin film equations
On the Cahn–Hilliard Equation with Degenerate Mobility
A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
Instabilities and singularities in Hele–Shaw flow
Diffusional phase transitions in multicomponent systems with a concentration dependent mobility matrix
On equilibrium solutions to nonlocal mechanistic models in ecology